Prove that the product of 2π
and 3/4
is an irrational number. Find the product and explain why the value is irrational. Explain your reasoning in 1–2 sentences.
To prove that the product of 2π and 3/4 is irrational, we can assume the opposite, that it is a rational number. We multiply 2π by 3/4 to get 3π/2, which is irrational since π is irrational and cannot be cancelled out.
To prove that the product of 2π and 3/4 is an irrational number, we first find the product:
2π x 3/4 = (2 x 3 x π) / 4 = 6π / 4 = (3π) / 2.
The product (3π) / 2 is irrational because π is an irrational number, and multiplying an irrational number by a non-zero rational number (in this case, 3/2) also results in an irrational number.